Finding the current in a simple series RL circuit.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Finding the stationary points of a cubic with two turning points

Finding lengths of sides of triangles

Finding the volumes of basic 3D shapes

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

Finding the stationary points of a cubic with two turning points

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Question asks student to find zeros of a quadratic equation - disguised as finding time for particle to reach a given position. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance. Coefficients of the quadratic are randomly chosen within linits which give one positive and one negative root.

Graph a linear or quadratic function and state its domain and range. Part of HELM Book 2.2.1.

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem. 

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem. 

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

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Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

Given the original formula the student enters the transformed formula

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Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Finding the product of a linear function of the form $mx+c$ and a cubic function of the form $ax^3+bx^2+cx+d$.

Finding the product of two linear functions of the form $mx+c$ and a quadratic function of the form $ax^2+bx+c$.

Finding the product of three linear functions of the form $mx+c$.

Finding the product of two linear functions of the form $mx+c$.

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Finding the coordinates and determining the nature of the stationary points on a polynomial function